Let's say you have a database full of each achievement, and a timestamp when you first earned it.
All it takes now, assuming both characters have the same timestamps on each achievement is a quick query on the account bound stuff to find two records with exact matching dates across all characters for a given realm, from there you can make the assumption that if characters 1,2,3,4 all got achievements X,Y,Z on the same day, that they're the same person (as even members of a raid would have different time stamps on non-raid things)
EDIT:
Also, If someone's "Harassing" you, report them. removing websites that let you pinpoint alts is not the problem, the person threatening, idle threats, and rolling new alts to circumvent your ignore list (all of the above are against the TOS) is the problem. The website is an accessory, and nothing more.